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LARGE STRAIN COMPOSITE MATERIALS IN
DEPLOYABLE SPACE STRUCTURES
Thomas W. Murphey
Space Vehicles Directorate, Air Force Research Laboratory
3550 Aberdeen Ave. SE, Kirtland AFB, NM 87117
[email protected]
SUMMARY
This paper investigates large strain composite materials in deployable space structures.
These structures balance material stiffness and foldability to achieve both compact
packaging and efficient deployed performance. Past approaches to achieve this
compromise are reviewed and new material developments are discussed. Materials are
compared based on metrics for packaged and deployed structural efficiency. Structural
architecture limitations are found to exist due to the low modulus and strain
combination of currently available passive materials. Large strain elastomeric resin
composite materials are shown to have the potential to eliminate these limitations.
Keywords: deployable structures, space structures, large strain composites
INTRODUCTION
Large strain materials have been used extensively by the deployable space structures
community to build reliable and highly compactable structures such as storable tubular
extendible masts (STEM)1-3, continuous longeron trusses4 and wrap-rib reflectors5,6
(Figure 1). While successful, these architectures all exhibit relatively low structural
hierarchy compared to alternate approaches and are limited in their potential structural
performance and sizes. For example, the STEM is a tube, the continuous longeron truss
is a truss of solid rods and the wrap-rib employs open-section beam elements. Increases
in hierarchy, such as trusses of tubes or trusses of trusses have not achieved flight
success with large strain material approaches. Such structures have been achieved with
mechanical approaches employing sliding contact (pin-clevis) joints. For example, the
deployable mesh reflector in Figure 2 uses complex mechanisms to form a perimeter
truss of tubes7. A contributing factor to this state is the less than sufficient combination
of modulus and strain available in traditional engineering materials as well as a poor
engineering understanding of how to best exploit available materials in flexure hinge
applications.
Suitable materials for large strain deployable structures must satisfy two conflicting
requirements. First, the materials must be capable of large strains for compact
packaging and design freedom. The architectures of Figure 1 are typically designed to
1.0-1.5% strain; however, strains of 4-5% would enable much greater design flexibility
and allow the implementation of architectures that are only feasible with larger strains.
For example, the architectures in Figure 3 and Figure 4 are only possible with larger
strain materials (these architectures require two to four times more strain than those in
Figure 1)8. Second, the materials must be stiff in the deployed configuration. Space
structures typically employ slender elements and shells that fail in buckling under
compressive loads and the primary material property governing this load is modulus.
Similarly, when loaded in tension, the material property of interest is modulus as it
determines deflections and structural modes of vibration. In considering materials for
deployable structures, it is important to realize that they do not need to be high modulus
in the packaged configuration. It is acceptable and often desirable if the material
modulus decreases during packaging so that less strain energy is stored. It is the
deployed material modulus (and density) that ultimately determines the structural mass
efficiency of a deployed structure. However, there is a trade between modulus for
deployed performance and strain for packaging performance and materials that are good
with one property are often poor with the other.
Several approaches have been researched to address this challenge. Most successful has
been the development of rigidizable composite materials by L’Garde Incorporated9,10,
ILC Dover LP11, and Composite Technology Development Incorporated12,13. These
companies developed carbon fiber based material systems with heat softenable matrix
materials. When heated, the materials can be folded to very large strains repeatedly
without degradation of their unfolded ability to resist buckling.10 The primary limitation
of these materials is the extreme challenge of engineering and testing the in space
heating and cooling systems they require. Either through test or analysis, demonstrating
uniform and sufficient heating without excessive power requirements is highly
challenging. The opposite problem of ensuring the structure remains cool enough to be
rigid on orbit is equally challenging. These heating and cooling systems also have
sufficient mass that the effective mass efficiency (modulus per mass metrics) of these
materials is greatly reduced. As a result, rigidizable structures with both compact
packaging and good deployed structural mass efficiency have rarely been achieved.
In light of these challenges, there is renewed interest in passive large strain materials:
those that do not require heating, cooling or other challenging thermal restrictions. The
current work investigates these materials.
a)
b)
c)
Figure 1: Space deployable structures using large strain materials: a) storable tubular
extendible masts1-3 on Hubble Space Telescope solar arrays, b) continuous longeron
mast (ATK-Able)4 c) Lockheed Martin wrap-rib reflector5,6.
Figure 2: The Northrop Grumman Astromesh parabolic mesh reflector with truss of
tubes structural hierarchy.7
a)
b)
c)
d)
Figure 3: Elastic loop folding proposed in Reference 8 showing single longeron and
truss deployment.
a) Packaged
b) Half Deployed
c) Fully Deployed
Figure 4: A monolithic concertina fold architecture proposed in Reference 8.
LARGE STRAIN COMPOSITE MATERIALS
Properties of materials commonly used for deployable structures are given in Table 1.
These properties are the results of standardized tests and they may not be appropriate for
flexure hinges (due to hinge thinness, biaxial stress states, etc.). Even so, they are used
here because they are the only properties available. Firehole Technologies
Incorporated’s Prospector:Composites was queried for materials with relatively high
strains to failure and modulus (unidirectional lamina properties in the fiber direction).
Where possible, compressive modulus test results were used over tensile modulus
(representing the deployed state) and flexure strain to failure was used over tensile or
compressive strain to failure (representing the packed state). In the absence of flexure
strain to failure data, compressive strain to failure was used. Properties of materials not
represented by Prospector:Composites were derived from a combination of rule of
mixtures, manufacturer data sheets and MatWeb online material database queries.
Generally desired material properties are straight forward to identify in tables of test
results. Higher modulus, lower density, greater strain and greater strength are typically
better. However, selection of the best material when more than one property must be
considered simultaneously is not as obvious. In these cases, analytically derived metrics
that are a combination of properties should be calculated to compare materials. In
Reference 14, Michael Ashby tabulates many of these metrics and material properties
and devises a simple logarithmic scale plot that allows consideration a several metrics at
the same time. The same plot style is adopted here as the data of Table 1 are plotted in
Figure 5 and Figure 6.
Assessing materials for deployable structures generally requires considering more than
one property at a time. In the deployed configuration, material stiffness and density are
important and these are plotted in Figure 5. In parts of the structure that must deform for
packaging, strain is also important and stiffness is plotted vs. strain in Figure 6. The
dashed lines in these plots represent constant values for the indicated metric and can be
parallel offset for greater or lower constant metric value contour lines. In the modulus
vs. density plot, materials towards the upper left corner of the plot (higher modulus and
lower density) are better. In the specific density vs. strain plot, materials towards the
upper right (higher modulus and larger strain) are better. The best material depends on
which metric is used to assess the materials.
Dashed line slopes correspond to different metrics. In the modulus vs. density plot, four
metrics are shown and one should be selected based on the application. However,
regardless of metric choice, all curves tell the same story: higher modulus carbon fiber
composites are best. If carbon fiber composites are neglected, proper material choice
depends on the metric and application and could be either S2 fiberglass or steel.
Material selection is not as straightforward when strain is considered. As shown in
Figure 6b, there is a relationship between the maximum combination of modulus and
strain such that higher modulus materials have lower strain capacities and the slope of
this front is parallel to the metric line E 2 . Material selection is further complicated by
the inappropriateness of the strain data. The deployable structures under consideration
here employ flexures or solid rods that when bent to small radii, are not represented by
standardized flexure or tensile tests. Further, it has been observed that thinner laminates
can accommodate higher strains without failure than thicker laminates of the same
material. The mechanisms for this response have not been determined, but are likely a
combination of nonlinear fiber response and structural support of the laminate
compressive side by the tensile side. Understanding the mechanics and failure
mechanisms in large strain bending of thin composites is an area of ongoing research.
Material Metrics for Deployed Structures
Material metrics for deployed trusses in beam and column applications are derived in
Reference 15. In bending applications, subscript b, the beam is designed to meet a
bending stiffness requirement and a bending strength requirement (local failure of a
longeron in buckling is assumed). In column applications, subscript c, the truss is
designed to meet global and local longeron buckling requirements and must carry a
compressive load over a length. In both cases failure is governed by buckling, which is
determined from the material modulus. As a result, metrics capturing the mass
efficiency of a deployed truss only involve material modulus and density (not strength).
Designing the above trusses, calculating their weight equations and extracting material
parameters results in the following material performance metrics,
b 
c 
E 3/5

E 2/3

,
(1)
.
(2)
These metrics are shown in Table 1 and Figure 5 and there is an order of magnitude
difference between the stiffer and lower strain materials and the less stiff and larger
strain materials. This directly translates into truss mass and even without increases in
hierarchy, great improvements in truss performance can be made by simply using more
efficient materials.
Metrics for non-truss cross-section beams that combine stiffness and strength are not
available; however, the metric for a stiffness designed beam of arbitrary cross-section in
bending is given in Reference 14 as,
beam 
E1/2

.
(3)
In this metric, the beam cross-sectional shape is fixed, but it can be scaled up or down to
change the cross-sectional area and it is applicable to architectures such as the STEM of
Figure 1. The metric is also applicable to the buckling of columns with similar cross
section constraints (e.g. a STEM used as a column).
The metric for a stiffness designed tension only tie element is,
beam 
E

.
(4)
Material Metrics for Material Deformation Base Deployable Structures
There are two common approaches to achieving efficient deployable structures.
Articulated combinations of pin-clevis, ball and socket and other sliding contact joints
are used in what is commonly called a mechanical approach. Second, material
deformation can be used to fold a structure. Often, either approach can be used to
achieve a similar deployed architecture. However, selection of deployment architecture
greatly reduces freedom in material selection and ultimately, deployed performance.
Deformable materials, such as S2 fiberglass reinforced epoxy are approximately four
times less efficient than a high modulus material such as M60J carbon fiber reinforced
epoxy. Even so, deformation based architectures have been highly successful, primarily
due to their lower cost. Deformation based architectures can avoid the design,
machining and assembly costs associated with having hundreds of hinges in a single
deployable structure.
There are also two basic approaches to material deformation based deployable
structures: distributed strain and concentrated strain. In the distributed strain approach,
material deformations are distributed as uniformly as possible throughout the structure.
This approach minimizes the maximum strain in the structure and is employed by the
STEM and continuous longeron masts architectures of Figure 1. Rigidizable materials
were developed to increase the material strain limits without sacrificing material
modulus. The increased strain limits of these materials enabled more complex
architectures, such as trusses of tubes, however, taking in account the reduced fiber
volume fraction and mass of thermal management systems results in an effective
deployed performance that is less than fiberglass. Consequently, rigidizable structures
have not been able to improve on the performance obtained by mechanical or other
material deformation based approaches.
In the concentrated strain approach, mechanical hinges are replaced with flexure hinges
that concentrate strains into discrete hinge locations. This allows less flexible but more
efficient materials to be used in the majority of the structure and the less efficient but
more flexible materials are used only in hinge locations. Two concentrated strain
deployable structures are shown in Figure 7.16-18
Simple material metrics for deformation based deployable structures based on stiffness
and strength are not readily derived. When strength is neglected, stiffness driven
structures become more slender and folding strains decrease; however, buckling loads
quickly approach zero. Thus, placing a maximum strain requirement on stiffness driven
designs tends to erroneously rate materials with lower strain limits better. This is an
artifact of strength being neglected and while strength does not often drive the design of
deployable structures, metrics that include strength provide more reasonable results. The
material metric for a strain limited distributed strain continuous longeron mast subjected
to a bending strength requirement and weight optimized is given in Reference 8 as,
 E 
clm 

2/3
.
(5)
Metrics derived for distributed strain architectures are not necessarily applicable to
concentrated strain architectures and efforts by the author to derive a simple
concentrated strain metric have not yielded concise results. The primary challenge is
that the goodness of a concentrated strain hinge material is always relative to the stiffer
material used elsewhere in the structure. For example, a concentrated strain architecture
that employs S2 fiberglass as the stiff material benefits very little from the higher
modulus of a T800 composite hinge. Also, hinge axial stiffness can be more or less
important depending on the cross-section of the stiffer elements in a truss. Tubes
generally require less stiff materials because the decrease in cross-sectional area
between a tube and a thin flexure is less than the change in cross-sectional area between
a solid rod and a thin flexure. Similar relations exist with material density, though to a
much lesser extent. In structures with relatively small hinges, the mass efficiency of the
structure is determined primarily by the stiffer parts of the structure, not the hinges. The
density of hinge materials of very high density (e.g. NiTi SMA) should not be
neglected, however, in comparing high and low modulus composites with
approximately the same density, this difference can be neglected.
Recognizing that a concentrated strain hinge metric should capture both material
stiffness and strain and to a lesser extent density allows potential metrics to be
considered. Plotting modulus vs. strain in the log-log style used thus far shows the
relative importance of modulus and strain in concentrated strain architectures, Figure 8.
These curves in these plots represent trusses of solid rods and trusses of tubes assembled
with rectangular flexure hinges. The strut material and cross-section are labelled on each
curve. The trusses were designed so that the longeron and flexure buckle at the same
time in the deployed configuration and when folded, the hinge is subjected to the strain
indicated by the plot. The lines are contours corresponding to a 5% decrease in truss
performance due to the introduction of hinges. Hinge materials are also shown on the
plots. The material data used in these plots was derived from constituent tensile
properties and rule of mixtures and does not correspond to that used in Table 1.
Materials that lie outward of a contour line for given architecture have more than
enough modulus and strain to achieve that architecture with less than a 5% performance
degradation. Materials on the inside may still work for those architectures, but more
than a 5% performance degradation will occur. Lines are truncated on the left side of
these plots because hinge lengths become excessively long and do not represent a
concentrated strain architecture.
The curves in Figure 8 have linear regions, but they are not all the same slope. Dashed
lines corresponding to potential metrics with modulus to the first power and strain to the
first, second, and third power are shown. Several conclusions can be drawn from these
plots. Trusses of tubes are feasible with a range of common materials. In trusses of
tubes, strain is more important and curves follow a slope (metric) typically close to
E 2 . Trusses of solid rods require a greater combination of modulus and strain,
however, strain is not weighted as heavily with low strain slopes typically close to
E 1.5 . Solid rod trusses with lower modulus struts (S2) are possible with current
materials, but efficient trusses with higher modulus M60J struts are not feasible with
existing materials.
Even though trusses of solid rods are less conducive to the concentrated strain approach,
there is still significant motivation to develop them. Solid rods are generally much lower
cost and package more compactly than tubes.
Table 1: Materials used in deployable structures and flexure hinges.
  E   E1 2
 E Plot 
Name (Gpa) (%) (kg/m3)


 
Material Dist. Strain Deployed E3 5 

E2 3 

 E 
23

Concentrated Strain  E 1.5 E 2
AS4/997 Unidirectional Prepreg 1
(Fv=60%) AS4 122 1.53 1,589 77.2 220 2,833 15,544
958 232 28.7 E‐glass/GPP45 Unidirectional Prepreg 1
(Fv=45%) E 30.0 1.55 1,881 15.9 92 1,028 5,133 319 58 7.18 HR40/350 Unidirectional Prepreg 1
(Fv=60%) HR 197 0.94 1,630 120 272 3,663 20,736
923 179 17.3 IM7/977‐3 Unidirectional 1
(Fv=62%) IM 154 1.17 1,586 96.9 247 3,249 18,095
935 196 21.2 M46J/2020 Unidirectional Prepreg M46J (Fv=60%)1 218 0.69 1,650 132 283 3,850 21,944
798 126 10.5 S2‐449/SP381 Unidirectional Prepreg 1
(Fv=50%) S2 49.2 3.68 1,850 26.6 120 1,406 7,258 803 347 66.6 T300/F655 Unidirectional Prepreg 1
(Fv=55 to 59%) T3 143 1.55 1,570 90.9 241 3,139 17,395
1,079 274 34.1 T800/MTM49‐3 Unidirectional Prepreg 1
(Fv=60%) T8 162 1.36 1,620 100 248 3,283 18,346
1,046 257 30.0 2
Al 7075‐T6 Al 71.7 0.70 2,810 25.5 95 1,160 6,142 225 42 3.53 NiTi SMA NT 72.0 5.00 6,500 11.1 41 503 2,663 361 805 180 Steel/Elastomeric 3
Resin SS/ER 86.0 4.00 3,926 21.9 75 926 4,963 580 688 138 IM7/Elastomeric Resin3 IM/ER 110 4.00 1,500 73.3 221 2,810 15,305
1,790 880 176 S2/Elastomeric Resin3 S2/ER 35.0 4.00 1,770 19.8 106 1,198 6,045 707 280 56.0 M60/ER 237 4.00 1,558 152 312 4,288 24,581
2,875 1,896 379 5,055 29,763
1,089 207 17.4 4,501 250 315 36.0 2
M60J/Elastomeric Resin M60J/Epoxy3 M60 354 0.70 1,682 211 354 SS 210 1.31 7,850 26.8 58 Qrtz 45.0 3.43 1,844 24.4 115 1,337 6,861 724 286 52.9 P120 498 0.29 1,826 273 386 5,710 34,389
702 78 4.23 K13 560 0.36 1,844 304 406 6,069 36,839
865 K13D2U/Epoxy Prospector:Composites, Developed by Firehole Technologies Inc. and hosted by IDES Inc., http://www.ides.com/prospector/composites.asp. 2
Matweb, Automation Creations Inc., http://www.matweb.com/. 3
Rule of mixtures using manufacturer datasheets. 121 7.26 2
Spring Steel 3
Quartz, Saint‐Gobain 3
P‐120S/Epoxy 3
1
792 K13
P120
Carbon
Fiber Composites
250
M60
M60/ER
Modulus, E (Gpa)
M46
HR
T8
IM
T3
AS4
SS
Metals
IM/ER
SS/ER
NT
Al
S2
Qrtz
Silicon Dioxide
S2/ER
E
25
1,000
10,000
Density,  (kg/m3)
Figure 5: Comparison of the structural mass efficiency of materials used in mechanical
and material deformation based deployable structures.
K13
P120
K13
P120
M60/ER
HR
T8
IM
T3
AS4
E2/3 /
20,000
M60
Al
250
IM/ER
Modulus, E (Gpa)
M46
S2
Qrtz
S2/ER
E
M46
SS
M60/ER
HR
IM
T8
T3
AS4
IM/ER
SS/ER
Al
NT
SS/ER
SS
S2
Qrtz
S2/ER
NT
E
2,000
a)
25
0
Strain , (m/m)
0
b)
0.002
0.020
Strain, (m/m)
Figure 6: Specific modulus or modulus and density plots vs. strain for a) distributed
strain and b) concentrated strain structures.
a)
b)
Figure 7: A concentrated strain a) truss of tubes16 and b) truss of solid rods17,18.
a)
b)
Figure 8: Modulus vs. strain plots for concentrated strain trusses of solid rods and tubes
in a) beam applications and b) column applications.
FUTURE LARGE STRAIN MATERIALS
The strain data used to generate Figure 6 and Figure 8 are subject to criticism because
they represent standardized test results, not laminate high strain bending test results.
References 19 and 20 indicate thin composite bending failure strains are actually greater
than standardized compressive or tensile tests results. These references also show
strengthening with thinning. There is a need for higher strain materials as well as test
methods and failure models to engineer flexure hinges made from these materials.
One approach to achieving passive (no heating required) large strain materials currently
under investigation is to exploit microbuckling in composites with large strain (100300%) elastomeric matrix materials. Under tensile or small compressive loads and prior
to microbuckling, straight fibers will generate considerable axial stiffness and result in
efficient materials for deployed structures. With larger compressive loads, fibers will
microbuckle and the elastomeric matrix will allow for large effective compressive
strains. Lower matrix stiffness will result in a lower bulk material compressive strength.
Even so, the Euler column buckling load of fibers in the absence of a matrix is
significant and can provide a useful strength for a deployed structure. Consider an array
of steel fibers (e.g. small diameter music wire) in a large strain silicone or polyurethane
matrix at 40% fiber volume fraction. This material is referred to here as steel composite
or steel/elastomeric resin. Assume the fibers microbuckle under compressive loads with
a wavelength that is 50 times the fiber diameter. Microbuckling will allow large
effective elastic strains (approximately 4%) in this composite material while
maintaining a compressive strength of 5.18 MPa. If the matrix stiffness is assumed to
increase the fiber Euler buckling load by a factor of four, the material strength would be
20.7 MPa. These results are independent of fiber diameter.
Similar materials have been demonstrated with carbon fibers and are shown in Figure 9.
While this example uses T300 fibers, materials based on higher modulus fibers are also
conceivable and are shown in Table 1 and the metric plots. As shown in Figure 6, such
materials have the potential to offer dramatically improved performance and eliminate
strain induced architectural limitations.
Understanding the matrix stiffness vs. strain vs. compressive strength requirements of
this approach and if it has the potential to be a better hinge material are the subject of
ongoing research. The concentrated strain metrics in Table 1 indicate the approach is
significantly better than existing materials.
a)
b)
c)
Figure 9: Carbon fibers embedded in a high strain elastomeric resin, a) folded, b)
unfolded and c) showing microbuckled wavelength (residual microbuckling is primarily
due to resin shrinkage during curing, coupon fabricated by Adherent Technologies, Inc.)
CONCLUSIONS
History has demonstrated the success of carbon and S2 glass fiber composite materials
in relatively simple distributed strain deployable structures. Concentrated strain
deployable structures that use less efficient flexible materials only in hinge locations
have the potential for greater efficiency, design freedom and compact packaging.
However, their implementation is limited by the low strain capacity of engineering
materials. These limitations could be eased with both, a better knowledge of the
foldability of currently available composite materials and the development of passive
high strain materials that exploit elastomeric resins and microbuckling.
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